What do his listeners mistakenly feel keeps them from falling into hell?

This is a
good question. Edwards assumes that his hearers do not know what situation they are in. They
mistakenly forget that they are sinners in the hands of an angry God, as the title of the sermon
makes clear. I would say that is the bulk of the sermon and where people are mistaken.
Therefore, Edwards is at pains to show them that the unconverted person is near hell. Here is a
quote:

So that every unconverted Man properly belongs to
Hell; that is his Place; from thence he is.

Here is
another:

The old Serpent is gaping from them. Hell opens
his Mouth wide to receive them; and if God should permit it, they would be hastily swallowed up
and lost.

The only thing that keeps the unconverted man
from hell is the good pleasure of God. Edwards then goes one to say that some people believe
that their prudence, care, or wisdom will save them. Edwards burst this opinion as well. He
writes:

There is this clear evidence that Mens own
Wisdom is no Security to them from Death.

In the end, not
ignorance, mans care, concern, or hard work can help people from hell. Therefore, the only
solution from falling into hell is to run away from hell (to God), which is exactly the way the
sermon ends.